Dissipation-induced topological insulators: A no-go theorem and a recipe

摘要: Nonequilibrium conditions are traditionally seen as detrimental to the appearance of quantum-coherent many-body phenomena, and much effort is often devoted their elimination. Recently this approach has changed: It been realized that driven-dissipative dynamics could be used a resource. By proper engineering reservoirs couplings system, one may drive system towards desired quantum-correlated steady states, even in absence internal Hamiltonian dynamics. An intriguing category equilibrium many-particle phases those which distinguished by topology rather than symmetry. A natural question thus arises: these topological states can achieved result dissipative Lindblad-type (Markovian) evolution? Beside its fundamental importance, it offer novel routes realization topologically-nontrivial quantum simulators, especially ultracold atomic gases. Here I give general answer for Gaussian quadratic Lindblad evolution, mostly concentrating on example 2D Chern insulator states. prove no-go theorem stating finite-range Lindbladian cannot induce finite-rate exponential decay unique pure state above 1D. construct recipe creating such exponentially-local dynamics, or mixed arbitrarily close via also address cold-atom realization, classification, detection Extensions other types insulators superconductors discussed.